High Order Asymptotic Preserving Deferred Correction Implicit-Explicit Schemes for Kinetic Models

Implicit-Explicit Schemes for BGK Kinetic Equations

In this work a new class of numerical methods for the BGK model of kinetic equations is presented. In principle, schemes of any order of accuracy in both space and time can be constructed with this technique. The methods proposed are based on an explicit-implicit time discretization. In particular the convective terms are treated explicitly, while the source terms are implicit. In this fashion ...

Asymptotic-preserving and positivity-preserving implicit-explicit schemes for the stiff BGK equation∗

We develop a family of second-order implicit-explicit (IMEX) schemes for the stiff BGK kinetic equation. The method is asymptotic-preserving (can capture the Euler limit without numerically resolving the small Knudsen number) as well as positivity-preserving — a feature that is not possessed by any of the existing second or high order IMEX schemes. The method is based on the usual IMEX Runge-Ku...

High order asymptotic preserving DG-IMEX schemes for discrete-velocity kinetic equations in a diffusive scaling

In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the porous media equation, the advectiondiffusion equation, and the viscous Burgers’ equation. Our approach is based on the micromacro reformulation of the kinetic...

High-Order LES Simulations using Implicit-Explicit Runge-Kutta Schemes

For many flow problems modeled by Large Eddy Simulation (LES), the computational meshes are such that a large number of the elements would allow for explicit timestepping, but the CFL-condition is highly limited by the smaller stretched elements in the boundary layers. We propose an implicit-explicit time-integration scheme that uses an implicit solver only for the smaller portion of the domain...

Asymptotic preserving boundary conditions for kinetic models